Ask question

Ask question

All categories

max2010maxim [7]

2 years ago

3

Mr. Mole left his burrow that lies below the ground and started digging his way at a constant rate deeper into the ground. After

555 minutes of descending at a rate of 1.81.81, point, 8 meters per minute, he was 13.513.513, point, 5 meters below the ground.
Let yyy represent Mr. Mole's altitude (in meters) relative to the ground after xxx minutes.

Complete the equation for the relationship between the altitude and number of minutes.

y=

1 answer:

Dmitrij [34]2 years ago

3 0

Answer:

The relation is:

y = -1.8t - 4.5

Step-by-step explanation:

A general linear model equation is given by the formula:

y = mx+c

As descending is dependent to time t , replace x with t

y = mt+c

Where m is the rate of descending in this question

We are given that:

Rate of descending = 1.8

As the altitude is related to rate of descending, and it is decreasing, so

m = -1.8

Substitute in the general equation:

y = -1.8t + c

We know that for t=5 , altitude y = -13.5 , substitute in the above equation to find c.

-13.5 = -1.8(5) +c

c = -4.5

Substitute m = -1.8 and c = -4.5 in the general equation to find the relation

y = mt +c

y = -1.8t - 4.5

You might be interested in

6. Two observers, 7220 feet apart, observe a balloonist flying overhead between them. Their measures of the

MaRussiya [10]

Answer:

The ballonist is at a height of 3579.91 ft above the ground at 3:30pm.

Step-by-step explanation:

Let's call:

h the height of the ballonist above the ground,

a the distance between the two observers,

$a_1$ the horizontal distance between the first observer and the ballonist

$a_2$ the horizontal distance between the second observer and the ballonist

$\alpha _1$ and $\alpha _2$ the angles of elevation meassured by each observer

S the area of the triangle formed with the observers and the ballonist

So, the area of a triangle is the length of its base times its height.

$S=a*h$ (equation 1)

but we can divide the triangle in two right triangles using the height line. So the total area will be equal to the addition of each individual area.

$S=S_1+S_2$ (equation 2)

$S_1=a_1*h$

But we can write $S_1$ in terms of $\alpha _1$ , like this:

$\tan(\alpha _1)=\frac{h}{a_1} \\a_1=\frac{h}{\tan(\alpha _1)} \\S_1=\frac{h^{2} }{\tan(\alpha _1)}$

And for $S_2$ will be the same:

$S_2=\frac{h^{2} }{\tan(\alpha _2)}$

Replacing in the equation 2:

$S=\frac{h^{2} }{\tan(\alpha _1)}+\frac{h^{2} }{\tan(\alpha _2)}\\S=h^{2}*(\frac{1 }{\tan(\alpha _1)}+\frac{1}{\tan(\alpha _2)})$

And replacing in the equation 1:

$h^{2}*(\frac{1 }{\tan(\alpha _1)}+\frac{1}{\tan(\alpha _2)})=a*h\\h=\frac{a}{(\frac{1 }{\tan(\alpha _1)}+\frac{1}{\tan(\alpha _2)})}$

So, we can replace all the known data in the last equation:

$h=\frac{a}{(\frac{1 }{\tan(\alpha _1)}+\frac{1}{\tan(\alpha _2)})}\\h=\frac{7220 ft}{(\frac{1 }{\tan(35.6)}+\frac{1}{\tan(58.2)})}\\h=3579,91 ft$

Then, the ballonist is at a height of 3579.91 ft above the ground at 3:30pm.

6 0

2 years ago

Line segment ON is perpendicular to line segment ML, and PN = 10.

Ne4ueva [31]

we know that

Triangle MOL is an isosceles triangle

because

$MO=OL=radius\ of\ circle=25\ units$

$ON=25\ units$

$ON=OP+PN\\ 25=OP+10\\ OP=25-10\\ OP=15\ units$

Find the base MP

Applying the Pythagorean Theorem in the right triangle MPO

$MO^{2} =MP^{2}+PO^{2}\\ MP^{2}=MO^{2}-PO^{2}\\ MP^{2}=25^{2}-15^{2}\\ MP^{2}=400\\ MP=20\ units$

$ML=2*MP\\ ML=2*20\\ ML=40\ units$

Find the area of triangle MOL

$A=\frac{1}{2}ML*PO\\ \\ A=\frac{1}{2}*40*15\\ \\ A=300\ unit^{2}$

therefore

the answer is

the area of triangle MOL is

$300$ square units

3 0

2 years ago

Read 2 more answers

Conservation of Species A certain species of turtle faces extinction because dealers collect truckloads of turtle eggs to be sol

JulijaS [17]

Answer:

The turtle population's rate of growth will be 32 turtles per year after 2 years and 248 per year after 6 years.

Ten years after the conservation measures are implemented the population will be 3260 turtles.

Step-by-step explanation:

To find the rate of growth of the turtle population at any time <em>t</em> you need to find $N'(t)$

$\frac{d}{dt}N(t)=\frac{d}{dt}(2t^3+3t^2-4t+1000)\\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\\frac{d}{dt}(2t^3)+\frac{d}{dt}(3t^2)-\frac{d}{dt}(4t)+\frac{d}{dt}(1000)\\\\\mathrm{Apply\:the\:Power\:Rule}:\quad \frac{d}{dx}\left(x^a\right)=a\cdot x^{a-1}\\\\N'(t)=6t^2+6t-4$

In particular, when t = 2 and t = 6, we have

$N'(2)=6(2)^2+6(2)-4=32\\\\N'(6)=6(6)^2+6(6)-4=248$

so the turtle population's rate of growth will be 32 turtles per year after 2 years and 248 per year after 6 years.

The turtle population at the end of the tenth year will be

$N(10)=2(10)^3+3(10)^2-4(10)+1000\\N(10)=3260 \:turtles$

3 0

2 years ago

A frog catches insects for his lunch. The frog likes to eat flies and mosquitoes in a certain ratio, which is shown in the diagr

avanturin [10]

Answer:

ON MONDAY: 35 mosquitos.

ON TUESDAY: 6 flies.

Step-by-step explanation:

As you can see in the diagram, the frog eats 3 flies for every 7 mosquitoes (for lunch). Then you can expresed this ratio as following:

3:7 or $\frac{3}{7}$

Based on the table:

-If the frog eats 15 flies on monday, then the number of mosquitos that it eats can be calculated as following:

$\frac{3}{7}=\frac{15}{mosquitoes}\\\\mosquitoes=\frac{15*7}{3}\\\\mosquitoes=35$

-If the frog eats 14 mosquitoes on tuesday, then the number of flies that it eats can be calculated as following:

$\frac{3}{7}=\frac{flies}{14}\\\\flies=\frac{14*3}{7}\\\\flies=6$

8 0

2 years ago

Pls explain your work!

mylen [45]

Answer:

find total volume to find what amount is 20%

hack, is put the 20% in alreadyy to find 20% volume

20%=1/5

so

vcone=1/3(hpir^2)

times thath by 1/5

vcone=1/15(hpir^2)

d/2=r

given

4.8=d

4.8/2=d/2=r=2.4

10=h

V=1/15(10pi2.4^2)

V=1/15(10pi5.76)

V=1/15(57.6pi)

V=3.84pi

V=12.0637 cubic inches=20% of vase

0.5 cubc inches per min

0.5 times t=12.0637

divide both sides by 0.5

t=24.1237

about 24 minutes

Step-by-step explanation:

6 0

2 years ago